Question

4^(x+1)-5*2^(x)+1<0

Answer 1

$displaystyle 4^{x+1}-5*2^{x}+1 textless 0 \ 4*4^x-5*2^{x}+1 textless 0 \ 4*(2^2)^x-5*2^x+1 textless 0 \ 4*2^{2x}-5*2^x+1 textless 0 \ 2^x=t, t textgreater 0 \ 4*t^2-5t+1 textless 0 \ D=5^2-4*4=25-16=9 \ t_1= frac{5-3}{4*2}= frac{1}{4} \ \ t_2= frac{5+3}{2*4}=1 \ 4(t-1)(t- frac{1}{4}) textless 0 \ tin( frac{1}{4}; 1) \ \ 2^x=t_1 \ 2^x= frac{1}{4} \ 2^x=2^{-2} \ x=-2 \ \ 2^x=t_2 \ 2^x=1 \ x=0 \ \ xin(-2;0)$